Use the image to answer the question.
An illustration shows a shape that appears as a horizontal rectangle and a vertical rectangle joined with a quarter circle. The length and width of both of the rectangles is 5 centimeters and 3 centimeters. The radius of the quarter circle is 3 centimeters. The overlapping lines, which include the right side of the top rectangle and the top of the bottom rectangle, are marked as dashed lines. A right angle symbol appears where the top of the bottom rectangle and the right side of the top rectangle meet.
You are designing a portion of your backyard for grass. You come up with the image shown. Solve using 3.14 as pi. What is the total area? Round to the nearest hundredth.
(1 point)
cm2
The total area can be calculated by finding the individual areas of the rectangles and the quarter circle, then adding them together.
Area of the top rectangle = length x width = 5 cm x 3 cm = 15 cm²
Area of the bottom rectangle = length x width = 5 cm x 3 cm = 15 cm²
For the quarter circle:
Radius = 3 cm
Area = πr²/4 = 3.14 x 3 cm x 3 cm / 4 = 7.065 cm²
Total area = 15 cm² (top rectangle) + 15 cm² (bottom rectangle) + 7.065 cm² (quarter circle) = 37.065 cm²
Therefore, the total area is approximately 37.07 cm².